The attack killed 45 people, including six policemen, and wounded more than 100, at least 30 critically, said Tariq Khan, a government official in the Bajur region.
Police say it may be the first time Islamic militants sent a woman to carry out a suicide attack in Pakistan.
Police said the victims were from various parts of Bajur who gather daily at the center to collect food tokens distributed by the World Food Program and other agencies to conflicted-affected people in the region. The people were displaced by an army offensive against Taliban militants in the region in early 2009.
The Pakistani Taliban claimed responsibility for Saturday's suicide attack in Khar, through its spokesman, Azam Tariq.
Bajur is on the northern tip of Pakistan's semiautonomous tribal belt, bordering Afghanistan and the so-called "settled" areas in Pakistan. It has served as a key transit point and hideout for al-Qaeda and the Taliban.
Prime Minister Syed Yousuf Raza Gilani condemned the bombing and said Pakistanis are "united against them."
The military first declared victory in Bajur following a six-month operation launched in late 2008. But the army was forced to launch a follow-up operation in late January this year and declared victory again about a month later. Still, violence has persisted.
The Associated Press contributed to this report